Various methods for estimating motion between two adjacent pictures in temporal direction are developed. For example, these methods include a block matching method, an optical flow method, a Pel-recursive method, and Bayesian method.
One solving method returns the optical flow method to an anisotropic diffusion equation (an expression described by partial differential equation).
For example, Xiao et al. proposed a method for suitably processing a boundary of motion using Bilateral Filtering. This method is disclosed in “Bilateral Filtering-Based Optical Flow Estimation with Occlusion Detection, J. Xiao, H. Cheng, H. Sawhney, C. Rao and M. Isnardi, ECCV2006”.
First, a method prior to Xiao is explained by referring to FIG. 2. In the following explanation, a motion vector representing a motion of each pixel is called a flow.
FIG. 2 is a schematic diagram showing a flow in one-dimension. In FIG. 2, a flow of each pixel between two adjacent pictures is previously estimated as shown in the left part. Furthermore, flow filtering that swung flows are clearly arranged by filtering is shown in the right part.
Next, Xiao et al. improved the prior method by a concept of Bilateral Filtering. This Xiao method is explained by referring to FIG. 3. As shown in FIG. 3, a weight of filtering is calculated as a weight of connection by adding three weights, i.e., a weight of position, a weight of difference between pixel values, and a weight of difference between flows. Briefly, Xiao proposed a flow filtering preserving a boundary of motion.
However, as shown in FIG. 4, if a flow of a source pixel is largely erroneous, the weight of difference between flows badly affects on the weight of connection. As a result, an error flow does not converge to a correct flow.